Math

Ratio Calculator

Simplify any ratio A:B to its lowest terms, or solve for the missing value in A:B = C:D. Two modes in one calculator.

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Ratio Formulas

Simplifying uses the greatest common divisor. Solving for an unknown uses cross multiplication.

Simplified A:B = (A/GCD) : (B/GCD)

A/B = C/D → D = (B × C) / A

Ratios in Everyday Contexts

Ratios appear constantly in everyday life. Screen aspect ratios describe width-to-height proportions: 16:9 is the standard for modern TVs and monitors, while 4:3 was the traditional format. A camera sensor with a 3:2 aspect ratio produces photos with three units of width for every two units of height.

In cooking, ratios are the foundation of many recipes. Classic vinaigrette uses a 3:1 ratio of oil to acid. Bread dough is often described by baker's percentages — ratios of each ingredient relative to total flour weight. Understanding ratios lets you scale recipes reliably without memorising specific quantities.

Map scales express the ratio between a distance on the map and the corresponding distance in the real world. A scale of 1:50,000 means one centimetre on the map equals 50,000 centimetres (500 metres) on the ground. Engineers and architects use similar scale ratios in technical drawings.

Frequently asked questions

What is a ratio?
A ratio is a comparison of two quantities that shows their relative sizes. It is written as A:B (read as A to B) or as a fraction A/B. Ratios do not have units — they express the relationship between two numbers. For example, a ratio of 3:1 means the first quantity is three times larger than the second. Ratios are used extensively in cooking (ingredient proportions), finance (debt-to-equity), photography (aspect ratios), and science (concentration ratios).
How do you simplify a ratio?
To simplify a ratio A:B to its lowest terms, find the greatest common divisor (GCD) of A and B, then divide both values by it. For example, to simplify 12:8, the GCD of 12 and 8 is 4. Dividing both by 4 gives 3:2. A ratio is fully simplified when the two numbers share no common factors other than 1. This process is analogous to reducing a fraction to its lowest terms.
What is the difference between a ratio and a proportion?
A ratio is a comparison of two quantities, while a proportion is a statement that two ratios are equal. If A:B = C:D, that is a proportion. Proportions are used to scale quantities while maintaining their relative relationship. For example, if a recipe uses a 2:3 ratio of oil to vinegar, you can scale it up using the proportion 2:3 = 4:6 = 6:9 and so on. The ratio describes the relationship; the proportion uses that relationship to solve scaling problems.
How do you solve for a missing value in a ratio?
If you have a proportion A:B = C:D and one value is unknown, you can solve using cross multiplication. For a missing D, cross multiply to get A × D = B × C, then solve for D = (B × C) / A. For example, if 3:4 = 9:?, cross multiply to get 3 × ? = 4 × 9 = 36, so ? = 12. This technique is the basis for solving many practical scaling problems in cooking, mapwork, and engineering.
What does it mean for a ratio to be equivalent?
Two ratios are equivalent if they simplify to the same lowest-terms ratio. The ratios 2:4, 3:6, 5:10, and 50:100 are all equivalent because they all simplify to 1:2. Equivalent ratios represent the same proportional relationship at different scales. When you scale a recipe up or down, mix paint colours in consistent proportions, or produce blueprints, you are working with equivalent ratios.
How are ratios used in financial analysis?
Financial ratios are among the most widely used analytical tools in business. The price-to-earnings ratio compares share price to annual earnings per share. The debt-to-equity ratio compares total liabilities to shareholder equity. The current ratio compares current assets to current liabilities to assess short-term liquidity. The gross margin ratio compares gross profit to revenue. These ratios allow analysts to compare companies of different sizes and to benchmark performance against industry averages.

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